Physics - Magnetism Question with Solution | TestHub

Two point charges A and B, having charges ${\mathrm{q}}_{\mathrm{A}}$ and ${\mathrm{q}}_{\mathrm{B}}$ in ratio $\frac{{\mathrm{q}}_{\mathrm{A}}}{{\mathrm{q}}_{\mathrm{B}}}=\frac{-(\sqrt{2}+1)}{\sqrt{2}-1}$, enter a uniform magnetic field given by $\overrightarrow{\mathrm{B}}=0$ for $\mathrm{x}<0\&\overrightarrow{\mathrm{B}}=-{\mathrm{B}}_0\hat{\mathrm{k}}$ for $\mathrm{x}>0$. Charges enter at origin making an angle $45^{\circ }$ with x-axis moving in xy plane as shown, one by one, and eventually, come out. During their motion the maximum x-coordinate acquired by both of them is equal. If their de-Broglie wavelengths are ${\lambda }_{\mathrm{A}}$ and ${\lambda }_{\mathrm{B}}$ respectively, find $\frac{{\lambda }_{\mathrm{A}}}{{\lambda }_{\mathrm{B}}}$. (Ignore interaction between A and B) ( ${\mathrm{q}}_{\mathrm{A}}$ is -ve )